Beyond Constructivism : Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

by Lesh, Richard A.; Doerr, Helen M.

• ISBN13: 9780805838220
• ISBN10: 0805838228
• eBook ISBN(s): 9781317438519
• Format: Paperback
• Copyright: 2003-05-01
• Publisher: Lawrence Erlbau
• More Book Details

Summary

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teachingfeatures an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

Table of Contents

Preface	ix
PART I: INTRODUCTION TO A MODELS AND MODELING PERSPECTIVE
Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving	3	(32)
Richard Lesh
Helen M. Doerr
Model Development Sequences	35	(24)
Richard Lesh
Kathleen Cramer
Helen M. Doerr
Thomas Post
Judith S. Zawojewski
Origins and Evolution of Model-Based Reasoning in Mathematics and Science	59	(12)
Richard Lehrer
Leona Schauble
Piagetian Conceptual Systems and Models for Mathematizing Everyday Experiences	71	(26)
Richard Lesh
Guadalupe Carmona
A Semiotic Look at Modeling Behavior	97	(28)
Paul E. Kehle
Frank K. Lester, Jr.
PART II: A MODELS AND MODELING PERSPECTIVE ON TEACHER DEVELOPMENT
A Modeling Perspective on Teacher Development	125	(16)
Helen M. Doerr
Richard Lesh
A Modeling Approach for Providing Teacher Development	141	(18)
Roberta Y. Schorr
Richard Lesh
A Modeling Approach to Describe Teacher Knowledge	159	(16)
Karen Koellner Clark
Richard Lesh
Task-Analysis Cycles as Tools for Supporting Students' Mathematical Development	175	(16)
Kay McClain
Explanations Why? The Role of Explanations in Answers to (Assessment) Problems	191	(14)
Martin van Reeuwijk
Monica Wijers
PART III: MODELS AND MODELING AS VIEWED BY HEAVY USERS OF MATHEMATICS
What Mathematical Abilities Are Needed for Success Beyond School in a Technology-Based Age of Information?	205	(18)
Richard Lesh
Judith S. Zawojewski
Guadalupe Carmona
The EPICS Model in Engineering Education: Perspectives on Problem-Solving Abilities Needed for Success Beyond Schools	223	(18)
William Oakes
Anthony G. Rud, Jr.
The Case for Cases	241	(14)
Geza Kardos
Introduction to an Economic Problem: A Models and Modeling Perspective	255	(10)
Charalambos D. Aliprantis
Guadalupe Carmona
A Models and Modeling Perspective on Technology-Based Representational Media	265	(14)
Tristan Johnson
Richard Lesh
A Models and Modeling Perspective on Skills for the High Performance Workplace	279	(18)
Melissa J. Dark
PART IV: MODELS AND MODELING IN PROBLEM SOLVING AND LEARNING
Ends-in-View Problems	297	(20)
Lyn English
Richard Lesh
A Models and Modeling Perspective on Problem Solving	317	(20)
Judith S. Zawojewski
Richard Lesh
A Models and Modeling Perspective on the Role of Small Group Learning Activities	337	(22)
Judith S. Zawojewski
Richard Lesh
Lyn English
Local Conceptual Development of Proof Schemes in a Cooperative Learning Setting	359	(24)
Guershon Harel
Richard Lesh
A Models and Modeling Perspective on Metacognitive Functioning in Everyday Situations Where Problem Solvers Develop Mathematical Constructs	383	(22)
Richard Lesh
Frank K. Lester, Jr.
Margret Hjalmarson
Interest, Identity, and Social Functioning: Central Features of Modeling Activity	405	(30)
James A. Middleton
Richard Lesh
Michelle Heger
PART V: MODELS AND MODELING BEFORE AND AFTER MIDDLE SCHOOL
Beyond Constructivism: An Improved Fitness Metaphor for the Acquisition of Mathematical Knowledge	435	(14)
Susan J. Lamon
Using a Translation Model for Curriculum Development and Classroom Instruction	449	(16)
Kathleen Cramer
Integrating a Models and Modeling Perspective With Existing Research and Practice	465	(14)
Marilyn Carlson
Sean Larsen
Richard Lesh
Models of Functions and Models of Situations: On the Design of Modeling-Based Learning Environments	479	(22)
Beba Shternberg
Michal Yerushalmy
PART VI: NEXT STEPS
From Problem Solving to Modeling: The Evolution of Thinking About Research on Complex Mathematical Activity	501	(18)
Frank K. Lester, Jr.
Paul E. Kehle
In What Ways Does a Models and Modeling Perspective Move Beyond Constructivism?	519	(38)
Richard Lesh
Helen M. Doerr
References	557	(26)
Author Index	583	(6)
Subject Index	589